Abstract
Competition is ubiquitous in microbial communities, shaping both their spatial and temporal structure and composition. Many classic minimal models, such as the Moran model, have been employed in ecology and evolutionary biology to understand the role of fixation and invasion in the maintenance of a population. Informed by recent experimental studies of cellular competition in confined spaces, we extend the Moran model to explicitly incorporate spatial exclusion through mechanical interactions among cells within a one-dimensional, open microchannel. The results of our spatial exclusion model differ significantly from those of its classical counterpart. The fixation/extinction probability of a species sharply depends on the species’ initial relative abundance, and the mean time to fixation is greatly accelerated, scaling logarithmically, rather than algebraically, with the system size. In non-neutral cases, spatial exclusion tends to attenuate the effects of fitness differences on the probability of fixation, and the fixation times increase as the relative fitness differences between species increase. Successful fixation by invasive species, whether through mutation or immigration, are also less probable on average than in the Moran model. Surprisingly, in the spatial exclusion model, successful fixations occur on average more rapidly in longer channels. The mean time to fixation heuristically arises from the boundary between populations performing either quasi-neutral diffusion, near a semi-stable fixed point, or quasi-deterministic avalanche dynamics away from the fixed point. These results, which can be tested in microfluidic monolayer devices, have implications for the maintenance of species diversity in dense bacterial ecosystems where spatial exclusion is central to the competition, such as in organized biofilms or intestinal crypts. The results may be broadly applied to any system displaying tug-of-war type dynamics with a region of quasi-neutral diffusion centered around regions of deterministic population collapse.
Author summary Competition for territory between different species has far reaching consequences for the diversity and fate of bacterial communities. In this study, we theoretically and computationally study the competitive dynamics of two bacterial populations competing for space in confined environments. The model we develop extends classical models that have served as paradigms for understanding competitive dynamics but did not explicitly include spatial exclusion. We find that spatial effects drastically change the probability of one species successfully outcompeting the other and accelerates the mean time it takes for a species to exclude the other from the environment. In comparison to the predictions of population models that neglect spatial exclusion, species with higher selective advantages are less heavily favoured to outcompete their rival species. Moreover, spatial exclusion influences the success of an invasive species taking over a densely populated community. Compared to classical well-mixed models, there is a reduction in the effectiveness of an invaders fitness advantage at improving the chances of taking over the population. Our results show that spatial exclusion has rich and unexpected repercussions on species dominance and the long-time composition of populations. These must be considered when trying to understand complex bacterial ecosystems such as biofilms and intestinal flora.
Competing Interest Statement
The authors have declared no competing interest.
Footnotes
↵* zilmana{at}physics.utoronto.ca, josh.milstein{at}utoronto.ca
